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1992issue C081-10

Occupancy and split-sample tests for average crossovers

A 24-year weekly history of a major industrial average was scored in two adjacent 12-year windows by holding each average-crossover stance until the opposite cross. Editorial reading: treat the crossover as a multi-week regime label, and accept the filter as an evaluated baseline only if those two windows agree.

  • Regime occupancy scores every week spent in a bullish or bearish stance after a moving-average-crossover, not only the week the lines meet.
  • Each occupied week was a directional hit when later price rose after a short-over-long stance, or fell after a short-under-long stance, at 1, 5, 13, 26, and 52 weeks ahead.
  • Close versus the 4-week exponential average was near even money for the following week in both 12-year windows.
  • Editorial reading: the 13-versus-26 pairing had the best mean directional score on the nearer horizons, but the two split-sample windows did not confirm each other, so that pairing is not an accepted evaluated baseline.
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Current trackMoving-average crossover108 readingsExponential smoothing117 readingsMoving average449 readings

Two adjacent weekly windows

A 24-year weekly history of a major industrial average was scored in two adjacent 12-year windows, 1968 to 1979 and 1980 to 1991. The split-sample window divides that long weekly history into two consecutive 12-year blocks to test whether a directional result repeats.

The filters compared the weekly close with 4-, 13-, 26-, and 52-week exponential averages and also compared those averages with one another. A moving average in this setting is a lookback summary of ordered prices used as an explicit baseline for later directional forecasts over a stated sampling interval.

An exponential average was defined as the prior average plus a smoothing weight times the gap between the latest price and that prior average, with the weight approximated as 2/(n+1). Exponential smoothing is that recursive blend of the latest price with the prior average.

A stance that lasts until the opposite cross

A moving-average-crossover turns the relative position of a faster average, or of price versus an average, into a bullish or bearish stance that lasts until the opposite cross. After a bullish cross the stance stayed bullish until a bearish cross, so every intervening week was scored, not only the week of the cross.

Regime occupancy is that choice to score every week spent in the stance, not only the week the lines meet, so a significance test has enough observations.

Directional hits at several horizons

Each occupied week was judged by whether later price moved with the short-versus-long alignment at 1, 5, 13, 26, and 52 weeks ahead. A directional hit counts the week correct when later price rises after a short-over-long stance, or falls after a short-under-long stance.

A chi-squared test marked a result as probably significant, significant, or highly significant when chance would produce it about once in 20, 100, or 1,000 repeats. Those chi-squared bands label how rarely a hit rate would appear under chance in about 20, 100, or 1,000 repeats of the same test.

13-week directional hit rate by DJIA average crossover, two 12-year windows

At a 13-week horizon the 1980–1991 window (right-hand bar of each pair) is the only sample that clears 60 percent, led by 13/26 at 62.3 percent and 4/52 at 61.5 percent as Merrill stated. The 1968–1979 window sits near even money on every pair, so the two adjacent decades do not confirm. Bar heights were read from Figure 4’s 40–50–60 percent scale; those two printed scores anchor the tallest 1980–1991 bars.
At a 13-week horizon the 1980–1991 window (right-hand bar of each pair) is the only sample that clears 60 percent, led by 13/26 at 62.3 percent and 4/52 at 61.5 percent as Merrill stated. The 1968–1979 window sits near even money on every pair, so the two adjacent decades do not confirm. Bar heights were read from Figure 4’s 40–50–60 percent scale; those two printed scores anchor the tallest 1980–1991 bars.Dow Jones Industrial Average · Weekly close, 13-week forecast horizon · 1968-01-01T00:00:00.000Z to 1991-12-31T00:00:00.000Z

Every occupied week after a bullish or bearish cross is scored, not just the crossover week. HS on the figure is Merrill’s chi-squared label for a result that would occur by chance once in 1,000 trials. Y-axis on the printed figure runs 40 percent at the top to 60 percent at the bottom.

What repeated, and what did not

Close versus the 4-week average was near even money for the following week in both 12-year windows.

The 13-week horizon produced the strongest cluster of directional hits. The first 12-year window otherwise showed little departure from chance at short and intermediate horizons.

Year-ahead scores for the longer pairs in the first window sat below 50 percent and were read as trend-change cues rather than trend continuation.

Averaging the 1-, 5-, 13-, and 26-week horizons, the 13-versus-26 pairing posted the best mean directional score, but the two 12-year windows did not confirm each other.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
12 of 57 in the Moving-average crossover track
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All readings on this track · 57 readings
  1. 1988Constructing moving averages: weights, smoothing and crossovers
  2. 1988Constructing breadth and average trend states
  3. 1989Evaluating an always-in-the-market moving-average crossover
  4. 1989Constructing symmetric market-breadth ratio accumulators
  5. 1989Objective crossover tests of Fibonacci wave ratios
  6. 1990Volume-adjusted moving average construction
  7. 1991Constructing a mechanical crossover on a synthetic price series
  8. 1991A two-speed breadth reading for intermediate market direction
  9. 1992A Deutschemark yield map with dual-average and relative-strength timing
  10. 1992Confirming currency-fund trends with a crossover and a filter
  11. 1992A moving-average slope filter for crossover signals
  12. 1992Occupancy and split-sample tests for average crossovers
  13. 1994Gold-mining seasonality and bond-fund duration switching
  14. 1994Price oscillator from two moving averages
  15. 1995Explicit exponential weights and binary entry filters
  16. 1996Currency futures crossover with slope, bond filter, and stop
  17. 1996Two-market average crossover entry with a fixed stop
  18. 1997Construction of a filtered three-average crossover
  19. 1998Two-group exponential average compression as a trend filter
  20. 1998Constructing r-squared trend filters with dual lookbacks
  21. 1998Moving-average length is a habit, not a secret
  22. 1999Solving the close that triggers a moving-average crossover
  23. 2000Kagi yang and yin control versus crossover noise
  24. 2000Constructing simple moving average crossover filters
  25. 2000Building a vertical-horizontal filter to gate trend signals
  26. 2000Two-average crossover as a check on trend following
  27. 2003Stacked exponential-average retracement entries and extreme stops
  28. 2003Evaluating oscillator thresholds against optimized crossovers
  29. 2004Constructing a semicycle trend-quality filter
  30. 2004Commodity subgroups labeled by crossover, support, or convergence
  31. 2004Full-window evaluation of crossover trend systems
  32. 2004Two-average trend filters as a classroom critique of indicator stacking
  33. 2005Three-layer confirmation from a moving-average cross, candles, and Q-stick
  34. 2005Charting put prices beside an equity breakdown
  35. 2005Range-gated moving-average crossover construction
  36. 2007Anticipating a simple-average crossover with a threshold-close
  37. 2007Anticipating moving-average crossovers one bar ahead
  38. 2007Lead-series moving-average crossovers with a stochastic and relative strength index
  39. 2007Next-bar SMA crossover hypotheses from theoretical crossing values
  40. 2007Anticipating a moving-average crossover before confirmation
  41. 2007A three-horizon moving-average stack as a construction problem
  42. 2007Confirming trend with regression slope and r-squared
  43. 2008Constructing a multi-timeframe smoothed crossover
  44. 2008Best-day clusters versus trend filters
  45. 2008Allied markets as a confirmation gate for crossover and breakout signals
  46. 2008Weekly exponential-average crossover as a mechanical trend case study
  47. 2010Evaluating a 200-day crossover as long, short, and stand-aside rules
  48. 2010Read a 10-and-40 trend on two neighboring time frames
  49. 2012Sampling unit as a first-class parameter on dual simple moving averages
  50. 2012Constructing index-ETF entries from volatility-index persistence
  51. 2013Moving-average baselines versus crossover signals
  52. 2013Constructing a typical-price and heikin-ashi crossover as one mechanical procedure
  53. 2016A three-gate checklist for longs after a sharp drop
  54. 2016Weekly inflation-ratio crossover for commodity regimes
  55. 2017Normalized Laguerre zero-axis warning as a two-marker construction
  56. 2019Range-weighted construction of an adaptive exponential moving average
  57. 2020Construct a second-pullback entry after a moving-average crossover
By fieldIndicators and filters682 readingsBy year1992115 readings
All 108 readings tagged Moving-average crossover
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